"My" is more appropriate when speaking about yourself to someone else. but both are actually correct, just when used in different ways. To expand a little bit on the difference between "my" and "her" in this case: "my" indicates that the "language abilities" you want to improve are your own. This is talking from a first person perspective (you are talking from your perspective and you own the abilities). "her" is appropriate if you are talking from the third person perspective or about another person. Be careful though. Speaking about yourself from the perspective of someone else (third person) too frequently will lead people to believe you are maybe a little crazy. "My" is more natural when you are simply describing yourself in general. Here are some different forms of stating similar things: I am an English teacher who wants to improve my language abilities. (introduction and describing yourself in first person) I am an English teacher and I want to improve my language abilities. (introduction and stating intent - first person) I am an English teacher who wants to improve her language abilities. (first person introduction and third person description of yourself - this is sort of odd) "(She is a ____, and) I am an English teacher who wants to improve her language abilities." (introduces both yourself and the other person and states you want to improve the language abilities of the other person.) One last note: ability - abilities . When talking about a specific language skill you would say "language ability" but when talking about many, multiple, or undefined skills you would say "language abilities". e.g - "My language abilities" - because we didn't specify which one and we would probably agree that there are many "My English language ability" - because we said it was the English one "My English language abilities" - implies all of the English ones (reading, writing, speaking, etc.)

The second is correct.

'wants' 'who' referes to 'an English teacher' ,thus the 3rd singular conjugation of verb 'want' in the present tense follows.

I am an English teacher who wants to improve my language abilities.